{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:AOC4FQE5UTHU2YVFAU5CRD6SYY","short_pith_number":"pith:AOC4FQE5","canonical_record":{"source":{"id":"2309.04103","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2023-09-08T03:46:50Z","cross_cats_sorted":["math.CO","math.MG"],"title_canon_sha256":"412c77c3ba95b9cc25d3a639e7ecd5b6e2d9faed2c2c81993859b796a581a349","abstract_canon_sha256":"b96506f9f2247e65edc32c01693a11217ea6366ae56bd9722d72c98cc7d14ca0"},"schema_version":"1.0"},"canonical_sha256":"0385c2c09da4cf4d62a5053a288fd2c63869c82d1c62ec053abfb444a0f1370b","source":{"kind":"arxiv","id":"2309.04103","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.04103","created_at":"2026-07-05T09:23:44Z"},{"alias_kind":"arxiv_version","alias_value":"2309.04103v2","created_at":"2026-07-05T09:23:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.04103","created_at":"2026-07-05T09:23:44Z"},{"alias_kind":"pith_short_12","alias_value":"AOC4FQE5UTHU","created_at":"2026-07-05T09:23:44Z"},{"alias_kind":"pith_short_16","alias_value":"AOC4FQE5UTHU2YVF","created_at":"2026-07-05T09:23:44Z"},{"alias_kind":"pith_short_8","alias_value":"AOC4FQE5","created_at":"2026-07-05T09:23:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:AOC4FQE5UTHU2YVFAU5CRD6SYY","target":"record","payload":{"canonical_record":{"source":{"id":"2309.04103","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2023-09-08T03:46:50Z","cross_cats_sorted":["math.CO","math.MG"],"title_canon_sha256":"412c77c3ba95b9cc25d3a639e7ecd5b6e2d9faed2c2c81993859b796a581a349","abstract_canon_sha256":"b96506f9f2247e65edc32c01693a11217ea6366ae56bd9722d72c98cc7d14ca0"},"schema_version":"1.0"},"canonical_sha256":"0385c2c09da4cf4d62a5053a288fd2c63869c82d1c62ec053abfb444a0f1370b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:23:44.502453Z","signature_b64":"wQg9L5JuETw/6F3WCJBg51JYDnBci2jrLTUWN400K9yu+fM252jfscL4UL/IMYUailn0JpTie452peWMOM0SCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0385c2c09da4cf4d62a5053a288fd2c63869c82d1c62ec053abfb444a0f1370b","last_reissued_at":"2026-07-05T09:23:44.501944Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:23:44.501944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2309.04103","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:23:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vmarU3SfFdZzIgl+rKixCc94omkA3QWzQ4AApvSZH+RAGv60KmDubC7+YNQsM0ckUpXKaYcVwtorsXUmeLYYDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T07:40:12.521314Z"},"content_sha256":"b231f18df370eb0014f5e13d64d686eaaabd00cdb60cc440f56734017c341e03","schema_version":"1.0","event_id":"sha256:b231f18df370eb0014f5e13d64d686eaaabd00cdb60cc440f56734017c341e03"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:AOC4FQE5UTHU2YVFAU5CRD6SYY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"New improvement to Falconer distance set problem in higher dimensions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO","math.MG"],"primary_cat":"math.CA","authors_text":"Kevin Ren, Ruixiang Zhang, Xiumin Du, Yumeng Ou","submitted_at":"2023-09-08T03:46:50Z","abstract_excerpt":"We show that if a compact set $E\\subset \\mathbb{R}^d$ has Hausdorff dimension larger than $\\frac{d}{2}+\\frac{1}{4}-\\frac{1}{8d+4}$, where $d\\geq 3$, then there is a point $x\\in E$ such that the pinned distance set $\\Delta_x(E)$ has positive Lebesgue measure. This improves upon bounds of Du-Zhang and Du-Iosevich-Ou-Wang-Zhang in all dimensions $d \\ge 3$. We also prove lower bounds for Hausdorff dimension of pinned distance sets when $\\dim_H (E) \\in (\\frac{d}{2} - \\frac{1}{4} - \\frac{3}{8d+4}, \\frac{d}{2}+\\frac{1}{4}-\\frac{1}{8d+4})$, which improves upon bounds of Harris and Wang-Zheng in dimens"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.04103","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2309.04103/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:23:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Miojm/7DRI37MzuZJWB+jly04zT/2z/EkTAGQKixthAZc2MzegN5NfFu838iiOifhB6BhwwqAzoe/X85ss43Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T07:40:12.521905Z"},"content_sha256":"33aa9153b1f544fb68e4561e2df77b7bf30fb3f5bebba702aa51e8d3f330f81c","schema_version":"1.0","event_id":"sha256:33aa9153b1f544fb68e4561e2df77b7bf30fb3f5bebba702aa51e8d3f330f81c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AOC4FQE5UTHU2YVFAU5CRD6SYY/bundle.json","state_url":"https://pith.science/pith/AOC4FQE5UTHU2YVFAU5CRD6SYY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AOC4FQE5UTHU2YVFAU5CRD6SYY/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-10T07:40:12Z","links":{"resolver":"https://pith.science/pith/AOC4FQE5UTHU2YVFAU5CRD6SYY","bundle":"https://pith.science/pith/AOC4FQE5UTHU2YVFAU5CRD6SYY/bundle.json","state":"https://pith.science/pith/AOC4FQE5UTHU2YVFAU5CRD6SYY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AOC4FQE5UTHU2YVFAU5CRD6SYY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:AOC4FQE5UTHU2YVFAU5CRD6SYY","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"b96506f9f2247e65edc32c01693a11217ea6366ae56bd9722d72c98cc7d14ca0","cross_cats_sorted":["math.CO","math.MG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2023-09-08T03:46:50Z","title_canon_sha256":"412c77c3ba95b9cc25d3a639e7ecd5b6e2d9faed2c2c81993859b796a581a349"},"schema_version":"1.0","source":{"id":"2309.04103","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.04103","created_at":"2026-07-05T09:23:44Z"},{"alias_kind":"arxiv_version","alias_value":"2309.04103v2","created_at":"2026-07-05T09:23:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.04103","created_at":"2026-07-05T09:23:44Z"},{"alias_kind":"pith_short_12","alias_value":"AOC4FQE5UTHU","created_at":"2026-07-05T09:23:44Z"},{"alias_kind":"pith_short_16","alias_value":"AOC4FQE5UTHU2YVF","created_at":"2026-07-05T09:23:44Z"},{"alias_kind":"pith_short_8","alias_value":"AOC4FQE5","created_at":"2026-07-05T09:23:44Z"}],"graph_snapshots":[{"event_id":"sha256:33aa9153b1f544fb68e4561e2df77b7bf30fb3f5bebba702aa51e8d3f330f81c","target":"graph","created_at":"2026-07-05T09:23:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2309.04103/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that if a compact set $E\\subset \\mathbb{R}^d$ has Hausdorff dimension larger than $\\frac{d}{2}+\\frac{1}{4}-\\frac{1}{8d+4}$, where $d\\geq 3$, then there is a point $x\\in E$ such that the pinned distance set $\\Delta_x(E)$ has positive Lebesgue measure. This improves upon bounds of Du-Zhang and Du-Iosevich-Ou-Wang-Zhang in all dimensions $d \\ge 3$. We also prove lower bounds for Hausdorff dimension of pinned distance sets when $\\dim_H (E) \\in (\\frac{d}{2} - \\frac{1}{4} - \\frac{3}{8d+4}, \\frac{d}{2}+\\frac{1}{4}-\\frac{1}{8d+4})$, which improves upon bounds of Harris and Wang-Zheng in dimens","authors_text":"Kevin Ren, Ruixiang Zhang, Xiumin Du, Yumeng Ou","cross_cats":["math.CO","math.MG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2023-09-08T03:46:50Z","title":"New improvement to Falconer distance set problem in higher dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.04103","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b231f18df370eb0014f5e13d64d686eaaabd00cdb60cc440f56734017c341e03","target":"record","created_at":"2026-07-05T09:23:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"b96506f9f2247e65edc32c01693a11217ea6366ae56bd9722d72c98cc7d14ca0","cross_cats_sorted":["math.CO","math.MG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2023-09-08T03:46:50Z","title_canon_sha256":"412c77c3ba95b9cc25d3a639e7ecd5b6e2d9faed2c2c81993859b796a581a349"},"schema_version":"1.0","source":{"id":"2309.04103","kind":"arxiv","version":2}},"canonical_sha256":"0385c2c09da4cf4d62a5053a288fd2c63869c82d1c62ec053abfb444a0f1370b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0385c2c09da4cf4d62a5053a288fd2c63869c82d1c62ec053abfb444a0f1370b","first_computed_at":"2026-07-05T09:23:44.501944Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:23:44.501944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wQg9L5JuETw/6F3WCJBg51JYDnBci2jrLTUWN400K9yu+fM252jfscL4UL/IMYUailn0JpTie452peWMOM0SCA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:23:44.502453Z","signed_message":"canonical_sha256_bytes"},"source_id":"2309.04103","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b231f18df370eb0014f5e13d64d686eaaabd00cdb60cc440f56734017c341e03","sha256:33aa9153b1f544fb68e4561e2df77b7bf30fb3f5bebba702aa51e8d3f330f81c"],"state_sha256":"d8ca68e5a1bdf3d9e1315ba668e379d0f088656c49b2f05eea63895c41e0df9b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dIs9mw32XgWD65XxtQt7BTgDpOQRl87Cq5WAQbSx9U7YSSgurLSB6iEW7J/z92YHS0fmMbeKQEr8QAoIf0u9CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T07:40:12.528168Z","bundle_sha256":"b6a4413e24bc49fbbfe427a308a07ea4b18d35cad0dbbb27bdb09a57fad163af"}}